Adomian (from the book): u(m+1) = L (-1 )(inverse)) k x^p u(m)

[volkan]

Adomian's Solving Frontier Problems of Physics; The Decomposition Method book, page 16, in the solution of the Example ,

u(m+1) = L (-1 )(inverse)) k x^p u(m)
u= Sum ( m = 0 to infinity) (L (-1 (inverse)) k x^p)^m * u(0)

I don't understand this. Can anyone help?

The statement underlined above I then given as,


Sum (m=0 to infinity) k^m x^(m p + 2 m) / (m p +2 m -1) (m p +2 m)

Thanks

 

[HallsofIvy]

Since I am not going to run out and buy the book, could you at least tell us if "L(-1) (inverse)" means- the inverse Laplace transform?

If it does, do you know what the Laplace transform of x^n is? What about the inverse transform?